If you have an active subscription, which is what was created when you activated on the first computer, you need to use the same LiveID on the subsequent activations. On the first PC, open OneCare and click Help and then About to see your Subscription ID. That is the LiveID to sign in with.
On the laptop, after removing any other security software, go to http://onecare.live.com and download/install the trial of OneCare. Once it is installed, open OneCare and click on the subscribe action/link. Sign in with your subscription LiveID and it will become part of your subscription.
-steve
Microsoft MVP Windows Live / Windows Live OneCare & Live Mesh Forum Moderator